Multiple-Input-Multiple-Output (MIMO) is an advanced antenna technique utilized in wireless systems (e.g., cellular communications networks) to improve spectral efficiency and thereby boost overall system capacity. For MIMO, a commonly known notation of (M×N) is used to represent the MIMO configuration in terms the number of transmit antennas (M) and the number of receive antennas (N). The common MIMO configurations used or currently discussed for various technologies are: (2×1), (1×2), (2×2), (4×2), (8×2), and (8×4). The MIMO configurations represented by (2×1) and (1×2) are special cases of MIMO, and they correspond to transmit diversity and receive diversity, respectively.
Using multiple antennas at the transmitter and the receiver can significantly increase system capacity. Specifically, transmission of independent symbol streams in the same frequency bandwidth, which is commonly referred to as Spatial Multiplexing (SM), achieves a linear increase in data rates with the increased number of antennas. On the other hand, by using space-time codes at the transmitter, reliability of the detected symbols can be improved by exploiting the so called transmit diversity. Both the SM scheme and the transmit diversity scheme assume no channel knowledge at the transmitter. However, in practical wireless systems such as the 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE), High Speed Downlink Packet Access (HSDPA), and WiMAX wireless systems, channel knowledge can be made available at the transmitter via feedback from the receiver to the transmitter. The transmitter can utilize this channel information to improve the system performance with the aid of precoding. In addition to beamforming gain, the use of precoding avoids the problem of an ill-conditioned channel matrix.
In practice, complete Channel State Information (CSI), or similar known channel properties, may be available for a wireless system using a Time Division Duplexing (TDD) scheme by exploiting channel reciprocity. However, for a wireless system using a Frequency Division Duplexing (FDD) scheme, complete CSI is more difficult to obtain. In a FDD wireless system, some kind of CSI knowledge may be available at the transmitter via feedback from the receiver. These wireless systems are referred to as limited feedback systems. There are many implementations of limited feedback systems such as, e.g., codebook based feedback and quantized channel feedback. 3GPP Long Term Evolution (LTE), High Speed Packet Access (HSPA), and WiMax recommend codebook based feedback for precoding. Examples of CSI are Channel Quality Indicator (CQI), Precoding Indicator (PCI) (which is also referred to as a Precoding Matrix Indicator (PMI)), and a Rank Indicator (RI). One type of CSI or a combination of different types of CSI are used by a network node (e.g., a base station such as, for instance, a Node B (NB) in a Universal Terrestrial Radio Access (UTRA) network or an evolved or enhanced Node B (eNB) in LTE) for one or more resource assignment related tasks such as, e.g., scheduling data transmissions to a User Equipment device (UE), rank adaptation of MIMO streams, precoder selection for MIMO streams, etc.
In codebook based precoding, a predefined codebook is defined both at the transmitter and at the receiver. The entries of the codebook, which are commonly referred to as precoding matrices, can be constructed using different methods, e.g., Grassmannian, Lloyd's algorithm, Discrete Fourier Transform (DFT) matrix, etc. Each precoder matrix is often chosen to match the characteristics of the N×M MIMO channel matrix H for a particular number of transmit antennas (M) and receive antennas (N), resulting in so-called channel dependent precoding, where N≥1 and M≥1. This channel dependent precoding is also commonly referred to as closed-loop precoding and essentially strives for focusing the transmit energy into a subspace which is strong in the sense of conveying much of the transmitted energy to the UE. In addition, the precoder matrix may also be selected to strive for orthogonalizing the channel, meaning that after proper linear equalization at the UE, the inter-layer interference is reduced. At the receiver, it is common to find the Signal to Interference plus Noise Ratio (SINR) with different codebook entries and choose the rank/precoding index that gives highest spectral efficiency (capacity).
In the 3GPP LTE standards, separate codebooks are defined for various combinations of the number of transmit antennas and the number of transmission layers. The latter is also referred to as a RI or rank information. For example, for four transmit antennas, a total of 64 precoding vectors and matrices are defined. Also, for each rank in the codebook for the scenarios of RI=1, 2, 3, and 4, 16 elements per rank are defined. The 3GPP standards do not specify what criteria the UE should use to compute the RI and/or the optimum precoding matrices/vectors. In LTE, the eNB scheduler decides the parameters such as, for example, modulation and code rate (transport block size), PMI, and rank information for the data transmission (i.e., on the Physical Downlink Shared Channel (PDSCH)). These parameters are sent to the UE through the Physical Downlink Control Channel (PDCCH). After transmitting the PDCCH, the data channel (i.e., the PDSCH) is also transmitted to the UE. In LTE, the UE may send feedback information related to the PDSCH on any of the uplink control or data channels (i.e., the PUCCH and the Physical Uplink Shared Channel (PUSCH)).
Table 1 below is a PMI codebook for four transmit antennas as defined in 3GPP TS 36.211 (version 8.0). In Table 1, the number of layers is the rank, which is also the number of independent streams. Also, un is the basis vector where n goes from 0 to 15.
TABLE 1CodebookNumber of layers νindexun12340u0 = [1 −1 −1 −1]TW0{1}W0{14}/{square root over (2)}W0{124}/{square root over (3)}W0{1234}/21u1 = [1 −j 1 j]TW1{1}W1{12}/{square root over (2)}W1{123}/{square root over (3)}W1{1234}/22u2 = [1 1 −1 1]TW2{1}W2{12}/{square root over (2)}W2{123}/{square root over (3)}W2{3214}/23u3 = [1 j 1 −j]TW3{1}W3{12}/{square root over (2)}W3{123}/{square root over (3)}W3{3214}/24u4 = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}]TW4{1}W4{14}/{square root over (2)}W4{124}/{square root over (3)}W4{1234}/25u5 = [1 (1 − j)/{square root over (2)} j (−1 − j)/{square root over (2)}]TW5{1}W5{14}/{square root over (2)}W5{124}/{square root over (3)}W5{1234}/26u6 = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over (2)}]TW6{1}W6{13}/{square root over (2)}W6{134}/{square root over (3)}W6{1324}/27u7 = [1 (−1 + j)/{square root over (2)} j (1 + j)/{square root over (2)}]TW7{1}W7{13}/{square root over (2)}W7{134}/{square root over (3)}W7{1324}/28u8 = [1 −1 1 1]TW8{1}W8{12}/{square root over (2)}W8{124}/{square root over (3)}W8{1234}/29u9 = [1 −j −1 −j]TW9{1}W9{14}/{square root over (2)}W9{134}/{square root over (3)}W9{1234}/210u10 = [1 1 1 −1]TW10{1}W10{13}/{square root over (2)}W10{123}/{square root over (3)}W10{1324}/211u11 = [1 j −1 j]TW11{1}W11{13}/{square root over (2)}W11{134}/{square root over (3)}W11{1324}/212u12 = [1 −1 −1 1]TW12{1}W12{12}/{square root over (2)}W12{123}/{square root over (3)}W12{1234}/213u13 = [1 −1 1 −1]TW13{1}W13{13}/{square root over (2)}W13{123}/{square root over (3)}W13{1324}/214u14 = [1 1 −1 −1]TW14{1}W14{13}/{square root over (2)}W14{123}/{square root over (3)}W14{3214}/215u15 = [1 1 1 1]TW15{1}W15{12}/{square root over (2)}W15{123}/{square root over (3)}W15{1234}/2
            P      PMI        =                  I        4            -              (                  2          ⁢                      u            PMI                    ⁢                                    u              PMI              H                        /                                                                            u                  PMI                                                            2                                      )              ,one could obtain the precoding matrix WPMI for different ranks by selecting/permuting the appropriate columns of matrix PPMI for the considered PMI, as given in 3GPP TS 36.211.
The 3GPP standards do not specify what criteria the UE should use to compute the RI and/or the optimum precoding matrices/vectors. Note that the received SINR at the output of the MIMO detector (Minimum Mean Square Error (MMSE), Maximum Likelihood Detector (MLD), etc.) is a function of channel matrix H, precoding matrix, the noise power spectral density, and the co-channel interference power.
FIG. 1 graphically illustrates the conventional approach for searching the full precoder codebook to find the preferred RI and PMI (PCI in High Speed Packet Access (HSPA)) for a four transmit antenna system. Note that in this approach the precoding codebook contains 16 elements per each rank (layers or streams) as per 3GPP Technical Specification (TS) 36.211 V8.0.0. This conventional approach illustrated in FIG. 1 is an exhaustive search of the full codebook (i.e., for all PCI and RI combinations). As illustrated, for the exhaustive search, the UE estimates the channel to thereby compute the channel coefficients for the channel matrix H. The UE computes the Signal to Noise Ratio (SNR) for each element, or entity, in the full codebook (i.e., for each PCI and RI combination). The UE computes the capacity (C) of the channel for each element in the full codebook using the formula C=log2 (1+SNR). The UE then finds or selects the PCI and RI combination that provides the maximum capacity (C). The exhaustive search involves many computations and is impractical to implement when there are a large number of codebook entries.
Issues with codebook based precoding in a closed-loop MIMO wireless system arise from the fact that the performance of the system generally improves with the cardinality (i.e., size) of the codebook. Specifically, at the receiver, the receiver must evaluate all possible precoding matrices for all possible ranks for a given MIMO configuration (M×N) and report a RI and a PCI for the best rank and precoding matrix to the transmitter every Transmit Time Interval (TTI) or every few TTIs. Evaluating all possible precoding matrices for all possible ranks is a computationally intensive process. For example, in four branch MIMO in LTE, the UE must search 64 precoding matrices (also referred to as precoding entities) for finding the best rank and precoding matrix. This search of the 64 precoding matrices increases power consumption, drains UE battery life, and consumes more memory and processing resources at the UE. Furthermore the network node serving the UE may not always use a full set of CSI (e.g., a full set of ranks and precoding matrices). In this case, if the UE reports CSI (e.g., a RI and a PCI) out of the full set of CSI (e.g., all possible ranks and precoding matrices), then the network node may need to spend more resources or perform additional processing to identity an appropriate CSI for scheduling the UE.
U.S. Patent Application Publication No. 2014/0072065 A1 entitled FINDING CHANNEL STATE INFORMATION WITH REDUCED CODEBOOK IN A MULTI-ANTENNA WIRELESS COMMUNICATION SYSTEM discloses a reduction in the search space of precoder elements by restricting the search space to lower rank precoder elements. While this approach is beneficial, there still remains a need for additional mechanisms for reducing the search space of precoder elements for a closed-loop MIMO wireless system.